Design of ℓ1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance

Mathematics

Dmitrii Ivanov¹  Oleg Granichin²  Vikentii Pankov³  Zeev Volkovich⁴ 

[1] Department of Information Systems Security, Samara National Research University, 443086 Samara, Russia;Laboratory «Control of Complex Systems», Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, 199178 St. Petersburg, Russia;Science Research and Educational Center “Mathematical Robotics and Artificial Intelligence”, Faculty of Mathematics and Mechanics, Saint Petersburg State University, 199034 St. Petersburg, Russia;Software Engineering Department, ORT Braude College, Karmiel 21982, Israel;

关键词: non-minimum phase system;    fractional delays;    unknown-but-bounded noise;    stabilizing controller;   

DOI  :  10.3390/math10010069

来源: DOAJ

【 摘 要 】

${\ell }_1$-regularization methodologies have appeared recently in many pattern recognition and image processing tasks frequently connected to ${\ell }_1$-optimization in the control theory. We consider the problem of optimal stabilizing controller synthesis for a discrete non-minimum phase dynamic plant described by a linear difference equation with an additive unknown-but-bounded noise. Under considering the “worst” case of noise, the solving of these optimization problem has a combinatorial complexity. The choosing of an appropriate sufficiently high sampling rate allows to achieve an arbitrarily small level of suboptimality using a noncombinatorial algorithm. In this paper, we suggest to use fractional delays to achieve a small level of suboptimality without increasing the sampling rate so much. We propose an approximation of the fractional lag with a combination of rounding and a first-order fractional lag filter. The suggested approximation of the fractional delay is illustrated via a simulation example with a non-minimum phase second-order plant. The proposed methodology appears to be suitable to be used in various pattern recognition approaches.

【 授权许可】

Unknown